The sine integral function is used to determine patterns of radiation in many settings. For example, it is used to find the power of an antenna, and for patterns of acoustical radiation. It is also used to find the diffusion of heat, electromagnetic waves, and vibrations in a membrane.
The sine integral function is also used in signal processing. Taking the electrical representation of a signal such as a sound or an image, electrical engineers manipulate the signal for desirable qualities such as clarity by using functions such as the sine integral function. Specifically, the sine integral function's oscillations cause a ringing artifact and overshoots to appear when the sinc function is used as a low-pass filter.
A low-pass filter is designed to let only low-frequency sounds through, and to cut off signals that are too high. The ideal low-pass filter would have a sharp cut-off at the appropriate point, with no tapering off; however, since this is impossible in real life, a truncated sinc function is often used instead because its shape approximates that of an ideal low-pass filter. Integrating that sinc function results in the sine integral function.
Spectroscopy, the study of the interaction between radiated energy in the form of waves and matter, also uses the sine integral function. The sine integral function is part of performing the Fourier transform calculations that separate raw data out into spectra in order to plot the variations over time or location. The waves can be of any type, from electromagnetic to optical to infrared.